Free Boolean algebras over unions of two well orderings

Given a partially ordered set P there exists the most general Boolean algebra which contains P as a generating set, called the free Boolean algebra over P. We study free Boolean algebras over posets of the form P=P₀∪P₁, where P₀, P₁ are well orderings. We call them nearly ordinal algebras.Answering a question of Maurice Pouzet, we show that for every uncountable cardinal κ there are κ² pairwise non-isomorphic nearly ordinal algebras of cardinality κ.Topologically, free Boolean algebras over posets correspond to compact 0-dimensional distributive lattices. In this context, we classify all closed sublattices of the product (ω₁+1)×(ω₁+1), showing that there are only ℵ₁ many types. In contrast with the last result, we show that there are ℵ₁² topological types of closed subsets of the Tikhonov plank (ω₁+1)×(ω+1).     

Numerical analysis of the azimuthal periodicity in the two lowest order modes of microstructured fibres applied to the precise determination of the cutoff wavelength

The azimuthal far-field analysis technique (AFFAT) is one of the only two methods reported to date, able to measure the cutoff wavelength λ_c in microstructured fibres (MOFs). The measurement is operated through a parameter D which is related to the modulation of the power crossing a rotating slit at the output of the tested fibre. In standard fibres, the criterion of the CEI/IEC 793-1-C7A normalised method (i.e., 2.25% of the output power carried by the second mode) is expressed by the unchanged −16.4 dB value of D(λ_c). In this paper, we show that this criterion is expressed in MOFs by a value of D which strongly depends on the geometrical parameters of the fibre and on the launching conditions at the input. However, we demonstrate that, with a slightly relaxed criterion corresponding to 10% of the output power carried by the second mode at λ_c, D remains close to −10 dB whatever the considered MOF. Thus, this constitutes a universal decision criterion allowing to determine λ_c in any classical MOF, by means of the AFFAT, with a very limited uncertainty.     

Ultrasonic elastography using sector scan imaging and a radial compression

Elastography is an imaging technique based on strain estimation in soft tissues under quasi-static compression. The stress is usually created by a compression plate, and the target is imaged by an ultrasonic linear array. This configuration is used for breast elastography, and has been investigated both theoretically and experimentally. Phenomena such as strain decay with tissue depth and strain concentrations have been reported. However in some in vivo situations, like prostate or blood vessels imaging, this set-up cannot be used. We propose a device to acquire in vivo elastograms of the prostate. The compression is applied by inflating a balloon that covers a transrectal sector probe. The 1D algorithm used to calculate the radial strain fails if the center of the imaging probe does not correspond to the center of the compressor. Therefore, experimental elastograms are calculated with a 2D algorithm that accounts for tangential displacements of the tissue. In this article, in order to gain a better understanding of the image formation process, the use of ultrasonic sector scans to image the radial compression of a target is investigated. Elastograms of homogeneous phantoms are presented, and compared with simulated images. Both show a strain decay with tissue depth. Then experimental and simulated elastograms of a phantom that contains a hard inclusion are presented, showing that strain concentrations occur as well. A method to compensate for strain decay and therefore to increase the contrast of the strain elastograms is proposed. It is expected that such information will help to interpret and possibly improve the elastograms obtained via radial compression.     

A convenient reagent for generation and stabilization of cationic methallylpalladium complexes containing nitrogen ligands

A convenient synthesis of the easily handled, air stable methallyloxyphosphonium salt [CH₂C(Me)CH₂⁻O-P(NMe₂)₃]⁺[(3,5-(CF₃)₂-C₆H₃)₄B]⁻5 is described. The utility of this reagent in the generation and stabilization of cationic η³-methallyl palladium complexes through oxidative addition reactions is illustrated by the preparation of the stable salts of [(η³-C₄H₇)Pd(NN)]⁺[(3,5-(CF₃)₂-C₆H₃)₄B]⁻ from Pd₂(dba)₃. The molecular structure of one of them has been determined by a single-crystal X-ray diffraction.     

Darstellung und eigenschaften von und reaktionen mit metallhaltigen heterocyclen XXII. Synthese, eigenschaften und kristallstruktur des sechsgliedrigen heterocyclus [(h-C5H5)NiSP(CH3)2]2 und dessen verhalten gegenüber alkinen

The heterocycle [(h⁵-C₅H₅)NiSP(CH₃)₂]₂ is obtained by treatment of (h⁵-C₅H₅)₂Ni with (CH₃)₂HPS in toluene and crystallizes monoclinic in the space group P2₁/c with Z = 2. The highly reactive three-membered ring (h⁵-C₅H₅)$\text{NiSP}$(CH₃)₂ which is a dissociation product of [(h⁵-C₅H₅)NiSP(CH₃)₂]₂, can be trapped with bis(methoxycarbonyl)acetylene to give the PS containing nickelacyclopentadiene (h⁵-C₅H₅)$\text{NiSP(CH}{}_3\text{)}{}_2\text{CRC}$R (R  CO₂CH₃).     

Synthesis and resolution of a new helically chiral azahelicene

Helically chiral azahexahelicene 3 was prepared in four steps using the Mizoroki-Heck coupling followed by classical oxidative photodehydrocyclisation. Resolution of this new chiral system was achieved through separation by HPLC providing (−)- and (+)-3 in high optical purity. The absolute configurations of (−)- and (+)-3 were assigned as M and P, respectively, by means of circular dichroism. Each of the hexacyclic systems (M)-(−)- and (P)-(+)-3 was reacted with boron tribromide to provide the corresponding helical pyridophenols in good yields.     

Copper(I)-doped Wyoming’s montmorillonite for the synthesis of disubstituted 1,2,3-triazoles

A new catalytic system based on copper(I)-doped Wyoming’s montmorillonite was elaborated. This system was studied and was found to catalyze the formation of 1,4-disubstituted 1,2,3-triazoles when starting from azides and alkynes. It was used for the synthesis of a few triazole derivatives to show its usefulness.     

Small perturbations of an interface for elastostatic problems

We consider the Lamé system for an elastic medium consisting of an inclusion embedded in a homogeneous background medium. Based on the field expansion method and layer potential techniques, we rigorously derived the asymptotic expansion of the perturbed displacement field because of small perturbations in the interface of the inclusion. We extend these techniques to determine a relationship between traction‐displacement measurements and the shape of the object and derive an asymptotic expansion for the perturbation in the elastic moment tensors because of the presence of small changes in the interface of the inclusion. Copyright © 2016 John Wiley & Sons, Ltd.     

Reynolds stress and vorticity in turbulent wall flows

Experimental measurements in a boundary layer and a large-eddy simulation of plane channel flow have been used to study the dynamics of vorticity and mass transport in the nearwall region. It was found that Reynolds stress generation occurs in the vicinity of quasi-streamwise vortices, and that smoke particles tend to be ejected from the wall near these vortical structures.     

Nonlinearities effects on optical MIMO systems

Optical Review - Multimode fibers (MMF) are enjoying a renewed attention boosted by recent advances in multimode complex nonlinear optics. Reason behind nonlinearity is occurred either due to...